692 
MR. G. F. 0. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
Mechanical Force Experienced by a Moving Point-Charge. 
10. The first case [ shall consider will be that of the motion of a point-charge, the 
mount of the charge being q. I shall deduce the mechanical force experienced 
by the charge. 
Since the charge is supposed to be concentrated into an infinitely small volume, 
and since the values of the quantities E', H', . . . belonging to the system which is 
acting upon q, do not in general change at infinitely rapid rates from one point 
of space to the other, we may regard those values as constant throughout the space 
occupied by q. We suppose, of course, also that none of the charges, electric or 
magnetic, due to the influencing system are within the small volume occupied by q. 
Thus p' = 0 and t = 0. Again, since by equation (45) the magnetic force H", and, 
therefore also the magnetic induction B", due to the charge q, is in circles round the axis 
of motion of q, it follows that the volume-integrals of B'^, B" 2 , B" 3 , taken throughout 
any portion of space bounded by a surface of revolution having the axis of motion for 
its axis, are all zero. Thus, since in general, C' is not infinite, the volume-integrals 
of the three components of VC'B" taken throughout the space bounded by an 
infinitely small surface of revolution enclosing q and having the axis of motion for its 
axis of figure, are all zero. If the surface of revolution is symmetrical fore and aft 
of the charge, then the volume-integrals of the components of VG'D ' all vanish 
because D" is radial. By supposition t" vanishes also. 
Thus if P now stand for the force experienced by the small region (of the form just 
mentioned) surrounding q, we have simply 
P = Je 'p'dco + jvCTB'f/ftj - jVGTD'cA, 
where the integrations are to be understood vectorially, and clw denotes an element of 
volume. 
On account of the constancy of E', B', and D' within the space considered, we have 
P = E' J p'dco + V 
(jc "do) B' - Y (Jg'W) D'. (64). 
The value of J p"du> is q. 
Since B" is in circles about the axis of motion G is also in similar circles. Hence 
JG clo) vanishes when applied to a region bounded by a surface of revolution. Thus 
the last term vanishes. 
In finding the value of JC f 'da), the form of the bounding surface is important. If, 
for instance, we take a small sphere whose centre is at q> its polar axis coinciding 
with the axis of motion, then there is a positive rc-component of the displacement 
